We construct a sequence of linear positive operators by means of the Erkus- Srivastava multivariable polynomials which include q- Lagrange polynomial operators discussed in [5] and the Lagrange Hermite polynomial operators considered in [1]. We study the Korovkin type theorems for the constructed operators by using summability techniques of statistical convergence and the power series method. We also define a k-th order Taylor generalization of the multivariable polynomials operator and investigate the approximation of k-th times continuously differentiable Lipschitz class elements.

In this research article, we construct a q-analogue of the operators defined by Betus and Usta (Numer. Methods Partial Differential Eq. 1-12, (2020)) and study approximation properties in a polynomial weighted space. Further, we modify these operators to study the approximation properties of differentiable functions in the same space and show that the mofidied operators give a better rate of convergence.